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It is complex and difficult to perform the vehicle scheduling of urban bus lines, which is important to reduce the operational cost and improve the quality of public transportation services. One has to assign vehicles to cover a set of trips contained in a timetable while minimizing multiple objectives that may conflict with each other. Existing approaches combine these objectives in a weighted fashion to form a single objective and then use a single-objective optimization approach to solve it. However, they can only produce one solution, and it is not easy to assign a proper weight for each objective to obtain a superior solution that can balance different objectives. In this paper, a methodology is presented to create a set of Pareto solutions for this problem. First, a set of candidate vehicle blocks is generated. Then, multiple block subsets are selected from this candidate set by an improved multiobjective genetic algorithm combined with a departure-time adjustment procedure to obtain multiple Pareto solutions. To encode a solution, we propose a coding scheme that has a relatively short coding length and low decoding complexity. This approach is applied to a real-world vehicle scheduling problem of a bus line in Nanjing, China. Experiments show that this approach is able to quickly produce satisfactory Pareto solutions that outperform the actually used experience-based solution.

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